International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 1.3, p. 29

Table 1.3.3.1 

B. Souvigniera*

aRadboud University Nijmegen, Faculty of Science, Mathematics and Computing Science, Institute for Mathematics, Astrophysics and Particle Physics, Postbus 9010, 6500 GL Nijmegen, The Netherlands
Correspondence e-mail: souvi@math.ru.nl

Table 1.3.3.1| top | pdf |
Automorphism groups of two-dimensional primitive lattices

LatticeMetric tensorBravais group
Hermann–Mauguin symbolGenerators
Oblique [\pmatrix{g_{11} & g_{12}\cr & g_{22}} ] 2 2: [\bar x, \bar y]
Rectangular [\pmatrix{g_{11} & 0 \cr & g_{22} } ] 2mm 2: [\bar x, \bar y]
    m10: [\bar x, y]
Square [\pmatrix{g_{11} & 0 \cr & g_{11} } ] 4mm 4+: [\bar y, x]
    m10: [\bar x, y]
Hexagonal [\pmatrix{g_{11} & -{{1}\over{2}} g_{11} \cr & g_{11} } ] 6mm 6+: [x - y, x]
    m21: [\bar x, \bar x + y]